2025/05/22 by Peng Yu, Yu, Peng, Yuan Zhong +7 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2505.16108
openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we present two brane-world-type solutions in a two-dimensional (2D) dilaton gravity model with singular space-time backgrounds. By employing a first-order superpotential formalism, we first construct the 2D analogues of the thick brane solution previously given by Gremm and analyze the corresponding linear scalar perturbations. We show that for a model with canonical scalar matter fields, the effective potential of the linear perturbation equation is a singular Pöschl--Teller~II type, which does not admit bound states. However, for a model with non-canonical scalar fields, the effective potential becomes an exactly solvable Pöschl--Teller~I potential, which has an infinite tower of normalizable bound states. We also present a second analytic solution inspired by the work of Girardello et al., but with non-canonical scalar field. In this case, the linear perturbation equation is a Schrödinger equation with the Eckart potential, which is also exactly solvable.